In this work the time-optimal global pules for the CZ and the C\(_2\) Z gate in the blockade regime were identified. The pulse durations of \(T\Omega _{\mathrm {max}}=7.612\)  for the CZ gate and \(T\Omega _{\mathrm {max}}=16.43\)  for the C\(_2\) Z gate improve even upon the traditional, non-global pulses [1]}, [2]} and upon the recently discovered global pulse for the CZ gate with \(T\Omega _{\mathrm {max}}= 8.585\)  [3]}. Due to the shortest possible pulse duration, all types of errors which become more detrimental for longer gate durations, like the decay of the Rydberg state or Doppler shifts of the laser frequency, are mitigated. Since the pulses are global, they can be realized by a single laser addressing all atoms simultaneously. No single-site addressability is needed, thus significantly simplifying the experimental requirements. Interestingly, for the CZ gate single site addressability even brings no speedup over the time-optimal global pulse, showing that single site addressability, which requires a more complex experimetal setup, is not always advantageous.
